Some theoretical results on the stability of uncertain pantograph differential equations

Article type: Research Article

Authors: Wang, Xiao^{a; b; *}

Affiliations: [a] School of Economics and Management, Beijing Institute of Petrochemical Technology, Beijing, China | [b] Beijing Academy of Safety Engineering and Technology, Beijing, China

Correspondence: [*] Corresponding author. Xiao Wang, School of Economics and Management, Beijing Institute of Petrochemical Technology, Beijing Academy of Safety Engineering and Technology, Beijing, China. E-mail: wangxiao2018@bipt.edu.cn.

Abstract: Uncertain pantograph differential equation is a new type of differential equations in uncertainty theory. In this paper, we first give the concept of uncertain pantograph differential equation. In addition, this paper aims at the stability of this type of differential equations. The concepts of stability in measure and stability in pth moment for uncertain pantograph differential equations are presented and the sufficient conditions for uncertain pantograph differential equations being stable in measure and in pth moment are derived. Finally, this paper also discusses the relationship between these two types of stability.

Keywords: Uncertain pantograph differential equation, stability in measure, stability in pth moment, uncertainty theory

DOI: 10.3233/JIFS-191148

Journal: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 4, pp. 4431-4439, 2020